Inattention to States and Characteristics
Chris Engh
TL;DR
This paper develops a generalized rational inattention framework that accounts for costly information about both payoff-relevant states $\theta$ and hedonic characteristics $\xi$ of choices. By introducing a two-term information cost with a tunable weight $\alpha$, the authors obtain a unique, interior weighted multinomial logit conditional choice probability $P(\xi|\theta)$. The inner problem is cast as entropic optimal transport (Schrödinger bridge) between the marginal over characteristics and the state prior, yielding existence and uniqueness of the Schrödinger potentials and a dual representation, while the outer problem over the marginal $P_ξ$ is strictly concave and reduces to a single, well-behaved convex optimization. The model delivers testable predictions through entry-based restrictions, offers a clean link to Maxwell–Boltzmann statistics when $\alpha=1$, and provides practical computation methods via fixed-point iterations, convex optimization, and Sinkhorn-type algorithms. Overall, it unifies state–action and menu-characteristic attention in a rigorous, tractable framework with sharp empirical implications for discrimination among products under uncertainty.
Abstract
We introduce a rational inattention model which produces a unique, interior, weighted multinomial logit conditional choice probability for an agent who acquires costly information about the hedonic characteristics (e.g. whether an insurance contract has high coverage) of their choices and about their payoff-relevant states (e.g. their risk of incurring a loss). As usual, the objective is to choose a joint distribution subject to one marginal constraint (``Bayes plausibility''). We approach the problem by re-writing it in terms of an inner problem of maximizing over \textit{two} constraints and an outer problem of choosing the ``optimal constraint.'' The inner problem is a Schrödinger bridge problem. The outer problem is strictly concave.